PLEASE HELPPP ME WITH THIS MATH PROBLEM

Question

Find the domain of the equations. Do not solve! It would be great if you showed step by step process :)

square root x-3 + square root x+1 = 3/5-x

Answer 1

First let me confirm that this is what we're dealing with? √(x-3) + √(x+1) = 3/ (5-x).

The first term requires x ≥ 3 to avoid the square root of a negative number. The second term requires x ≥ -1, already made more restrictive by the first condition. The third term requires x ≠ 5 to avoid an infinite discontinuity. In interval notation, then, the Domain = [3, 5) ∪ (5, ∞).